6. (10%) Solve the following coupled differential equation. x+(a+By-aBx=0 y"-(a+8)x'-aBy=0,a＞0.8＞0,a≠β x(0)=0,x'(0)=1 y(0)=0,y'(0)=0.

7. (20%) Assume we have collected the data from four types of sensors four times from two experiments. Put these data in the form of matrix A and B. Check if matrix A and matrix B are diagonalizable. If it is diagonalizable, compute a matrix P such that BP is a diagonal matrix and compute the determinant of A4-5A2+2I or B4-5B2+2I. I is an identity matrix.